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I know that, for a single, two-level categorical covariate, like sex={Male, Female}, the linear regression coefficients are about difference in means. It's like the t test. Does the quantile regression do a similar thing with medians (assuming modelling the 50 percentile)? And if I model change between two groups (A-B) ~ Sex, I mean the differences between them, like in the paired t test, is this now about median difference or difference in medians?

Katikarnata
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  • https://stats.stackexchange.com/questions/251600 shows that quantile regression minimizes a particular loss function and estimates a specified quantile of the conditional distribution. – whuber Jun 08 '20 at 22:28
  • Thank you. I noticed that link you cited. I'm just searching for an explanation for "non-statisticians". In this case it seems, that if the dependent variable is change from baseline, it estimates median (for 2nd quartile/50th percentile) of change, so, for a single 2-category covariate the outcome is quite similar to the Wilcoxon paired test involving the pseudo-median on symmetric distribution. – Katikarnata Jun 08 '20 at 22:42
  • It comes down to what your notation means. I can't determine what "model change between two groups (A-B) ~ Sex" is trying to refer to. – whuber Jun 08 '20 at 22:46
  • I'm sorry for not being precise. I have measurements done at two time points, t0 (B) and t1 (A). I want to assess the median change between them, like the paired Wilcoxon test does, so my outcome is A-B (post_value - pre_value). If there are no covariates, I assume it's roughly similar to the pseudo-median of change the Wilcoxon signed rank procedure returns. If I add a 2-category variable, like sex, it becomes "adjusted for covariate", now I have median change for males and median change for females. Well, this is about medians, not pseudomedians, but for symmetric data it should be similar. – Katikarnata Jun 08 '20 at 22:56

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